Acoustics in one dimension

This notebook demonstrates running the Clawpack Fortran code and plotting results from a Jupyter notebook, and illustration of the behavior of various methods and limiters on the same problem.

This notebook can be found in $CLAW/apps/notebooks/classic/acoustics_1d_example1/acoustics_1d_example1.ipynb

The 1-dimensional acoustics equations \(q_t + Aq_x = 0\) is solved in the interval \(-1 \leq x \leq 1\) with extrapolation boundary conditions.

The density rho and bulk modulus K are specified in setrun.py but can be changed below.

Have plots appear inline in notebook:

In [1]:

%pylab inline

Populating the interactive namespace from numpy and matplotlib

Check that the CLAW environment variable is set. (It must be set in the Unix shell before starting the notebook server).

In [2]:

import os
try:
    CLAW = os.environ['CLAW']
    print "Using Clawpack from ", CLAW
except:
    print "*** Environment variable CLAW must be set to run code"

Using Clawpack from  /Users/rjl/git/clawpack

Module with functions used to execute system commands and capture output:

In [3]:

from clawpack.clawutil import nbtools

Compile the code:

In [4]:

nbtools.make_exe(new=True)  # new=True ==> force recompilation of all code

Executing shell command:   make new
Done...  Check this file to see output:
compile_output.txt

Make documentation files:

In [5]:

nbtools.make_htmls()

See the README.html file for links to input files...
README.html

Run the code and plot results using the setrun.py and setplot.py files in this directory:

First create data files needed for the Fortran code, using parameters specified in setrun.py:

In [6]:

nbtools.make_data(verbose=False)

Now run the code and produce plots. Specifying a label insures the resulting plot directory will persist after later runs are done below.

In [7]:

outdir,plotdir = nbtools.make_output_and_plots(label='1')

Executing shell command:   make output OUTDIR=_output_1
Done...  Check this file to see output:
run_output_1.txt
Executing shell command:   make plots OUTDIR=_output_1 PLOTDIR=_plots_1
Done...  Check this file to see output:
plot_output_1.txt
View plots created at this link:
_plots_1/_PlotIndex.html

Display the animation inline:

Clicking on the _PlotIndex link above, you can view an animation of the results.

After creating all png files in the _plots directory, these can also be combined in an animation that is displayed inline:

In [8]:

import clawpack.visclaw.JSAnimation.JSAnimation_frametools as J
anim = J.make_anim(plotdir, figno=1, figsize=(6,4))
anim

Out[8]:


Once Loop Reflect

Adjust some parameters to explore the methods in Clawpack

The animation above was computed using the default parameter values specified in setrun.py, which specified using the high-resolution method with the MC limiter. See the README.html file for a link to setrun.py.

We can adjust the parameters by reading in the default values, changing one or more, and then writing the data out for the Fortran code to use:

In [9]:

import setrun
rundata = setrun.setrun()

print "The left boundary condition is currently set to ",rundata.clawdata.bc_lower
print "The right boundary condition is currently set to ",rundata.clawdata.bc_upper

The left boundary condition is currently set to  ['extrap']
The right boundary condition is currently set to  ['extrap']

Periodic boundary conditions

Change the boundary conditions and write out the data. Then rerun the code.

In [11]:

rundata.clawdata.bc_lower = ['periodic']
rundata.clawdata.bc_upper = ['periodic']

# also extend the time over which the solution is computed and plotted:
rundata.clawdata.num_output_times = 40
rundata.clawdata.tfinal = 2.0

rundata.write()

outdir, plotdir = nbtools.make_output_and_plots(verbose=False)
anim = J.make_anim(plotdir, figno=1, figsize=(6,4))
anim

Out[11]:


Once Loop Reflect

Reflecting wall boundary conditions

Change the boundary conditions and write out the data. Then rerun the code.

In [12]:

rundata.clawdata.bc_lower = ['wall']
rundata.clawdata.bc_upper = ['wall']

rundata.write()

outdir, plotdir = nbtools.make_output_and_plots(verbose=False)
anim = J.make_anim(plotdir, figno=1, figsize=(6,4))
anim

Out[12]:


Once Loop Reflect

Things to try:

  • Use print rundata.clawdata to see what parameters can be set. Also print rundata.probdata to see what problem-specific paramaters are available.
  • Change the density rho or the bulk modulus K and see what effect this has.
In [13]:

def print_material():
    rho = rundata.probdata.rho
    K = rundata.probdata.K
    Z = sqrt(K*rho)
    c = sqrt(K/rho)
    print "The density rho = %g and bulk modulus %g give" % (rho,K)
    print "  speed of sound c = %g" % c
    print "  impedance Z = %g" % Z
print_material()

The density rho = 1 and bulk modulus 4 give
  speed of sound c = 2
  impedance Z = 2

In [14]:

rundata.probdata.rho = 4.
rundata.write()
print_material()

outdir, plotdir = nbtools.make_output_and_plots(verbose=False)
anim = J.make_anim(plotdir, figno=1, figsize=(6,4))
anim

The density rho = 4 and bulk modulus 4 give
  speed of sound c = 1
  impedance Z = 4

Out[14]:


Once Loop Reflect